Enter a small room and notice two guards standing in front of you. Naturally you're not interested in waiting for a doctor to arrive. As a result you'll have to get rid of them both. Start off by approaching a guard with a gun. You must stop directly in front of him, so he'll try to hit you with his weapon. Wait for a right moment to perform a countermove in order to kill him [#41]. Sadly you won't be allowed to take his weapon.
Choose your Shiv blade from your inventory quickly, assuming that you've been clever enough to smuggle this weapon from the prison block. Defeating the second guard [#42] shouldn't be a big problem, however prevent him from cornering you. Once he's gone inspect both bodies and pick up a magnetic card. You can also heal yourself using a nearby NanoMED station.
Start off by going towards the left door [#43]. If you've helped Shabby in getting rid of Molina, you will have the correct passcode needed to open this door. Thankfully Riddick will type in the numbers automatically. Explore your surroundings. You'll find a useless scalpel, as well as a cigarette pack (12 - Basilica Interior Detail 6).
Return to the main room of the infirmary and this time proceed to the door on your right. Use the recently obtained keycard to open the door. Be careful, though. The second you open the door you're going to be attacked by a third guard [#44]. I would recommend blocking frequently and looking for ways to perform counterattacks. This will allow you to end this duel without any health losses.
Proceed to a new room and once you're inside go to your right. You will soon reach an area where you'll find a very large medical station [#45]. Using this device will allow you to increase your health bar by one unit (square). Additionally, your current health will be restored. Once this is done use a nearby ladder to get to a new area.
Proceed forward and enter a small room. You will end up standing above the infirmary. Keep heading straight, BUT the second you notice a door opening in front of you take cover behind the nearest crate [#46]. Don't worry, because you'll perfectly safe, even though it's not dark here. Wait for the guard to move past you and surprise him from the back. Snap his neck and don't even bother hiding his body. Instead take a few credits.